Conditional modeling of antibody titers using a zero-inflated poisson random effects model: application to Fabrazyme^®

Abstract

Patients that are exposed to biotechnology-derived therapeutics often develop antibodies to the therapeutic, the magnitude of which is assessed by measuring antibody titers. A statistical approach for analyzing antibody titer data conditional on seroconversion is presented. The proposed method is to first transform the antibody titer data based on a geometric series using a common ratio of 2 and a scale factor of 50 and then analyze the exponent using a zero-inflated or hurdle model assuming a Poisson or negative binomial distribution with random effects to account for patient heterogeneity. Patient specific covariates can be used to model the probability of developing an antibody response, i.e., seroconversion, as well as the magnitude of the antibody titer itself. The method was illustrated using antibody titer data from 87 male seroconverted Fabry patients receiving Fabrazyme^®. Titers from five clinical trials were collected over 276 weeks of therapy with anti-Fabrazyme IgG titers ranging from 100 to 409,600 after exclusion of seronegative patients. The best model to explain seroconversion was a zero-inflated Poisson (ZIP) model where cumulative dose (under a constant dose regimen of dosing every 2 weeks) influenced the probability of seroconversion. There was an 80% chance of seroconversion when the cumulative dose reached 210 mg (90% confidence interval: 194–226 mg). No difference in antibody titers was noted between Japanese or Western patients. Once seroconverted, antibody titers did not remain constant but decreased in an exponential manner from an initial magnitude to a new lower steady-state value. The expected titer after the new steady-state titer had been achieved was 870 (90% CI: 630–1109). The half-life to the new steady-state value after seroconversion was 44 weeks (90% CI: 17–70 weeks). Time to seroconversion did not appear to be correlated with titer at the time of seroconversion. The method can be adequately used to model antibody titer data.